{"title":"On the System of Nonlinear Rational Difference Equations","authors":"Qianhong Zhang, Wenzhuan Zhang","volume":88,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":702,"pagesEnd":706,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9998174","abstract":"
This paper is concerned with the global asymptotic
\r\nbehavior of positive solution for a system of two nonlinear rational
\r\ndifference equations. Moreover, some numerical examples are given
\r\nto illustrate results obtained.<\/p>\r\n","references":"[1] M.P. Hassell and H.N. Comins, Discrete time models for two-species\r\ncompetition, Theoretical Population Biology, Vol. 9, no. 2,1976, pp.\r\n202\u2013221.\r\n[2] J.E. Franke and A.A. Yakubu, Mutual exclusion versus coexistence for\r\ndiscrete competitive Systems, Journal of Mathematical Biology, Vol.30,\r\nno. 2,1991, pp. 161\u2013168.\r\n[3] Marwan Aloqeili, Dynamics of a rational difference equation, Appl.\r\nMath. Comput., Vol. 176, no. 2, 2006, pp. 768\u2013774.\r\n[4] C. Cinar, On the positive solutions of the difference equation xn+1 =\r\nxn\u22121\r\n1+xnxn\u22121\r\n, Appl. Math. Compt. Vol.150, 2004, pp. 21\u201324.\r\n[5] C. Cinar, On the positive solutions of the difference equation xn+1 =\r\nxn\u22121\r\n1+axnxn\u22121\r\n, Appl. Math. Compt., Vol. 158, no.3,2004, pp. 809\u2013812.\r\n[6] C. Cinar, On the positive solutions of the difference equation xn+1 =\r\nxn\u22121\r\n\u22121+axnxn\u22121\r\n, Appl. Math. Compt., Vol. 158, no.3, 2004, pp. 793\u2013797.\r\n[7] C. Cinar, On the positive solutions of the difference equation xn+1 =\r\naxn\u22121\r\n1+bxnxn\u22121\r\n, Appl. Math. Compt., vol.156, 2004, pp. 587\u2013590.\r\n[8] B. Iricanin and S. Stevic, Some Systems of Nonlinear Difference Equations\r\nof Higher Order with Periodic Solutions, Dynamics of Continuous,\r\nDiscrete and Impulsive Systems. Series A Mathematical Analysis, Vol.\r\n13, No. 3-4, 2006, pp. 499\u2013507.\r\n[9] G. Papaschinopoulos and C.J. Schinas, On a system of two nonlinear\r\ndifference equations, J. Math. Anal. Appl. Vol. 219, 1998, pp. 415\u2013426.\r\n[10] D. Clark and M. R. S. Kulenovic, A coupled system of rational\r\ndifference equations, Comput Math Appl., Vol. 43, 2002, pp. 849\u2013867\r\n.\r\n[11] D. Clark, M. R. S. Kulenovic and J. F. Selgrade, Global asymptotic\r\nbehavior of a two-dimensional difference equation modelling competition,\r\nNonlinear Analysis, Vol. 52, 2003, pp. 1765\u20131776.\r\n[12] Q. Zhang, L. Yang and J. Liu, Dynamics of a system of rational\r\nthird-order difference equation, Advances in Difference Equations 2012,\r\n2012: 136, pp. 1\u20138.\r\n[13] J. Diblik, B. Iricanin, S. Stevic and Z. Smarda, On some symmetric\r\nsystems of difference equations, Abstract and Applied Analysis, Vol. 2013,\r\n2013, Article ID 246723,pp. 1\u20137.\r\n[14] Q. Din, M.N. Qureshi and A. Q. Khan, Dynamics of a\r\nfourth-order system of rational difference equations, Advances in\r\nDifference Equations, Vol.2012, 215, 2012, pp.1\u201315.\r\n[15] T. F. Ibrahim and Q. Zhang, Stability of an anti-competitive system of\r\nrational difference equations, Archives Des Sciences, Vol. 66, 2013, pp.\r\n44\u201358.\r\n[16] V.L. Kocic and G. Ladas, Global behavior of nonlinear difference\r\nequations of higher order with application , Kluwer Academic Publishers,\r\nDordrecht, 1993.\r\n[17] M.R.S. Kulenovic and O. Merino, Discrete dynamical systems and\r\ndifference equations with mathematica, Chapman and Hall\/CRC, Boca\r\nRaton, London, 2002.\r\n[18] T.F. Ibrahim, Two-dimensional fractional system of nonlinear difference\r\nequations in the modeling competitive populations, International Journal\r\nof Basic & Applied Sciences, Vol.12, no. 05, 2012, pp. 103\u2013121.\r\n[19] K. Liu , Z. Zhao, X. Li and P. Li, More on three-dimensional systems of\r\nrational difference equations, Discrete Dynamics in Nature and Society,\r\nVol. 2011, Article ID 178483, 2011.\r\n[20] E.M.E. Zayed and M.A. El-Moneam, On the global attractivity of two\r\nnonlinear difference equations, J. Math. Sci., Vol. 177, 2011, pp. 487\u2013499.\r\n[21] N. Touafek and E.M. Elsayed, On the periodicity of some systems of\r\nnonlinear difference equations, Bull. Math. Soc. Sci. Math. Roumanie,\r\nVol. 2, 2012, pp. 217\u2013224.\r\n[22] N. Touafek and E.M. Elsayed, On the solutions of systems of rational\r\ndifference equations, Mathematical and Computer Modelling, Vol. 55,\r\n2012, pp. 1987\u20131997.\r\n[23] S. Kalabusic, M.R.S. Kulenovic and E. Pilav, Dynamics of\r\na two-dimensional system of rational difference equations of\r\nLeslie\u2013Gower type, Advances in Difference Equations, 2011,\r\ndoi:10.1186\/1687-1847-2011-29.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 88, 2014"}